/*
 *                               POK header
 *
 * The following file is a part of the POK project. Any modification should
 * be made according to the POK licence. You CANNOT use this file or a part
 * of a file for your own project.
 *
 * For more information on the POK licence, please see our LICENCE FILE
 *
 * Please follow the coding guidelines described in doc/CODING_GUIDELINES
 *
 *                                      Copyright (c) 2007-2021 POK team
 */

/* @(#)s_cbrt.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#ifdef POK_NEEDS_LIBMATH

#include "math_private.h"
#include <libm.h>
#include <types.h>

/* cbrt(x)
 * Return cube root of x
 */
static const uint32_t B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
    B2 = 696219795;                   /* B2 = (664-0.03306235651)*2**20 */

static const double
    C = 5.42857142857142815906e-01,  /* 19/35     = 0x3FE15F15, 0xF15F15F1 */
    D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
    E = 1.41428571428571436819e+00,  /* 99/70     = 0x3FF6A0EA, 0x0EA0EA0F */
    F = 1.60714285714285720630e+00,  /* 45/28     = 0x3FF9B6DB, 0x6DB6DB6E */
    G = 3.57142857142857150787e-01;  /* 5/14      = 0x3FD6DB6D, 0xB6DB6DB7 */

double cbrt(double x) {
  int32_t hx;
  double r, s, t = 0.0, w;
  uint32_t sign;
  uint32_t high, low;

  GET_HIGH_WORD(hx, x);
  sign = hx & 0x80000000; /* sign= sign(x) */
  hx ^= sign;
  if (hx >= 0x7ff00000)
    return (x + x); /* cbrt(NaN,INF) is itself */
  GET_LOW_WORD(low, x);
  if ((hx | low) == 0)
    return (x); /* cbrt(0) is itself */

  SET_HIGH_WORD(x, hx); /* x <- |x| */
                        /* rough cbrt to 5 bits */
  if (hx < 0x00100000)  /* subnormal number */
  {
    SET_HIGH_WORD(t, 0x43500000); /* set t= 2**54 */
    t *= x;
    GET_HIGH_WORD(high, t);
    SET_HIGH_WORD(t, high / 3 + B2);
  } else
    SET_HIGH_WORD(t, hx / 3 + B1);

  /* new cbrt to 23 bits, may be implemented in single precision */
  r = t * t / x;
  s = C + r * t;
  t *= G + F / (s + E + D / s);

  /* chopped to 20 bits and make it larger than cbrt(x) */
  GET_HIGH_WORD(high, t);
  INSERT_WORDS(t, high + 0x00000001, 0);

  /* one step newton iteration to 53 bits with error less than 0.667 ulps */
  s = t * t; /* t*t is exact */
  r = x / s;
  w = t + t;
  r = (r - t) / (w + r); /* r-s is exact */
  t = t + t * r;

  /* retore the sign bit */
  GET_HIGH_WORD(high, t);
  SET_HIGH_WORD(t, high | sign);
  return (t);
}
#endif
